To make the pesto: In a food processor, combine the basil, arugula, jalapeño, 1 clove of garlic, the toasted nuts, parmesan, and 1/4 cup olive oil. Season with salt. Pulse until a sauce forms, adding 1-2 tablespoons water if needed to thin.
Bring a large pot of salted water to a boil. Add the pasta and cook according to package directions until al dente. Just before draining, remove 1/2 cup of the pasta cooking water. Drain and add the pasta right back into the hot pot.
Add the pesto and 1/2 cup coconut milk to the pasta, tossing to combine. Thin the pasta as desired with the reserved pasta cooking water.
Meanwhile, make the shrimp: Heat 2 tablespoons olive oil in a large skillet over medium heat. Add the butter, shrimp, 2 tablespoons Cajun seasoning, and a big pinch of pepper. Cook on both sides until seared, about 2-3 minutes per side.
Stir in the remaining 3 cloves of garlic and cook until fragrant, about 30 seconds. Remove from the heat, stir in the 1 tablespoon lemon juice.
Toss the cooked shrimp with the pesto pasta. Serve immediately and enjoy!